The half-reactions and their standard Gibbs free energy changes are given by:
Fe2++2e−→Fe
ΔG1⊖=−2FX
Fe3++3e−→Fe
ΔG2⊖=−3FY
The required half-reaction is:
Fe3++e−→Fe2+
ΔG3⊖=−1FEFe3+/Fe2+⊖
This reaction is obtained by subtracting the first reaction from the second reaction:
ΔG3⊖=ΔG2⊖−ΔG1⊖
−FEFe3+/Fe2+⊖=−3FY−(−2FX)
−FEFe3+/Fe2+⊖=−3FY+2FX
EFe3+/Fe2+⊖=3Y−2X
Answer: 3Y−2X